Assessing directional effects in spatial data.

Abstract

A variable is measured at two locations separated by a given distance. Are the values more similar to each other if the locations are oriented in one direction than another? This question has application to studies of human genetics, epidemics, and acid rain. One obvious analytic approach, regression on latitude and longitude, fails when data are non-directional (isotropic) but spatially autocorrelated. Moreover, although non-zero slope implies similarity between neighbours, the converse is not true. IDIFF, a statistic derived from Moran's coefficient of spatial autocorrelation, is developed to detect general directional effects that apply to the collection of data points. Simulations suggest that, when data have isotropic spatial autocorrelation but are incorrectly assumed to be independent, IDIFF will at worst reject too little. IDIFF has good power to distinguish epidemics that spread non-directionally from those that spread in a favoured direction.